If the cost price of 8 articles is equal to the selling price of 6 articles, then what is the profit percentage?

Options

A. 0.25
B. 0.375
C. 0.3333
D. 0.2

Answer

To find the profit percentage when the cost price of 8 articles is equal to the selling price of 6 articles, we can follow these steps:

### Step 1: Define Variables
Let the cost price (CP) of one article be \( x \). Therefore, the cost price of 8 articles is:
\[ \text{Cost Price of 8 articles} = 8x \]

Let the selling price (SP) of one article be \( y \). Therefore, the selling price of 6 articles is:
\[ \text{Selling Price of 6 articles} = 6y \]

### Step 2: Set Up the Equation
According to the problem, the cost price of 8 articles is equal to the selling price of 6 articles:
\[ 8x = 6y \]

### Step 3: Solve for Selling Price
From the equation \( 8x = 6y \), we can express \( y \) in terms of \( x \):
\[ y = \frac{8x}{6} = \frac{4x}{3} \]

### Step 4: Calculate Profit
The profit for selling 6 articles can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
The cost price of 6 articles is:
\[ \text{Cost Price of 6 articles} = 6x \]
Thus, the profit is:
\[ \text{Profit} = 6y - 6x \]
Substituting \( y \):
\[ \text{Profit} = 6\left(\frac{4x}{3}\right) - 6x = 8x - 6x = 2x \]

### Step 5: Calculate Profit Percentage
The profit percentage is calculated based on the cost price:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{2x}{6x}\right) \times 100 = \left(\frac{2}{6}\right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
Thus, the profit percentage is:
\[ \boxed{33.33\%} \]